This invention generally relates to electronic circuits. In particular, the invention relates to performing dual complex multiplication and complex division using a common circuit.
In electronic circuits, many different types of operations need to be performed. Two of the operations that may need to be performed is complex division and complex multiplication. In complex division, one complex number, such as a+jb, is divided by a second complex number, such as c+jd, as per Equation 1.
                                          (                          a              +                              j                ⁢                                                                  ⁢                b                                      )                                (                          c              +                              j                ⁢                                                                  ⁢                d                                      )                          =                                            (                                                a                  ⁢                                                                          ⁢                  c                                +                                  b                  ⁢                                                                          ⁢                  d                                            )                                      (                                                c                  2                                +                                  d                  2                                            )                                +                      j            ⁢                                          (                                                      b                    ⁢                                                                                  ⁢                    c                                    -                                      a                    ⁢                                                                                  ⁢                    d                                                  )                                            (                                                      c                    2                                    +                                      d                    2                                                  )                                                                        Equation        ⁢                                  ⁢        1            
In complex multiplication, one complex number, such as a+jb, is multiplied by a second complex number, such as c+jd, as per Equation 2.(a+jb)*(c+jd)=(ac−bd)*j(ad+bc)  Equation 2
Complex divisions and multiplications are necessary in many applications. A common application is in communications applications. In these systems, much of the processed information is in complex format requiring complex divisions and multiplications. To illustrate, data is commonly transmitted on an in-phase and quadrature carrier as complex data symbols.
Although complex division and multiplication can be performed by differing circuits, in many applications using two circuits is undesirable. In an integrated circuit environment, two circuits use up valuable silicon space. In a circuit board environment, two circuits require more components as well as requires more circuit board space.
Accordingly, it is desirable to have a circuit which can perform complex division and multiplication.